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Full text of "Scientific Papers - Vi"

1915]                  THE THEORY OF  THE HELMHOLTZ RESONATOR
Thus in general by (18)
____'__ ;____= _ ^     _ 1           (2n + 1} c2
Xn-i/Xn ~n  I            n
while for n  1
2 = - 2 + I - f c2 + terms in c3,
in accordance with (21).    When n = 0
Vn
 =  1 + c2 4- ic + terms in c3.
Using these values in (15), we see that, so far as c2 inclusive, 2 (outside) =(-l + c2 + w)P0
r.         1        5C2
-f P0
-    a
In like manner for the form of %n appropriate to the inside
, }==__________
Xn(C)    1.3.5...
so that in general
Zn + J.
j + 3
and
This suffices for n = I and onwards.    When n = 0 %   ___2 h _l__-cll
r^;~   c^j1   15   525} 
Accordingly, so far as c2 inclusive,
$ (inside) = 2 {P0 (/i) + Px (/*) + ...+ Pn (/*)}
369
ri/Xn-n-1        +n + l     (?i + l)a(2n-l)'.........^
.(22)
.(23)
.(24)
.(25)
.(26) .(27)
.(28)
R. VI.
.(29) 24
9!